Questions asked by Duncan T.

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• Find the area enclosed by the line y=4x and the curve y=x^2?
  
• Find the area enclosed by the line y=4x and the curve y=x^2?
  
• Integrate( 2/x+5secxtanx-6cosec^2x+4^x+8)dx?
  
• Integrate #(3x^2+cosx)/(x^3+sinx)#?
  
• Integrate (x/2+5secxtanx-6csc^2x+4^x+8)?
  
• Find the length of the tangent from the point (5,7) to the circle x^2+y^2-4x-6y+9=0 ?
  
• Find the inverse of the matrix [6 -2 -3] [-1 8 -7] [4 -4 6] ?
  
• Find the length of the tangent from the point (5,7) to the line x^2+y^2-4x-6y+9=0 ?
  
• With the help of a clear illustration explain the structure of the atmosphere ?
  
• Differentiate the following function in respect to x: y=√x+1/√x ?
  
• 2. A farmer has 10000m fencing wire with much to fence three sides of his rectangular farm,the fourth side being existing fence of his neighbour.find in metres the dimension of the field of the largest possible area that can be enclosed ?
  
• Divide 15 into two parts such that the square of one multiplied by the eighth of the other is maximum.find the two parts?
  
• The gradient of a curve at any point (x y) is 7-2x.Given that the curve passes through(3,2) find the equation of the curve?
  
• A car starts from rest and moves a distance of 5m in t seconds,where s=1/6t^3+1/4t^2.what is its acceleration when t=0,t=2?
  
• Solve the following systems of simultaneous equations using the inverse matrix of Gauss Jordan X1+2x2+3x3=3? 2x1+4x2+5x3=4? 3x1+5x2+6x3=8?
  
• Use Cramer's rule to solve the simultaneous equations: #4x-y+3z=11," " 2x+z =5 and -3x+2z+y=5#?
  
• Find the focus and directrix of the parabola #y=2a(x-a)^2#?
  
• Determine the equation of the hyperbola having its centre at the origin transverse axis at the x axis eccentricity being √7/2?
  
• Show that the circles #4x^2+4y^2-10x+16y+2=0#,and #4x^2+4y^2+12x+6y-26=0# are orthogonal?
  
• Find the equation of the circle with radius 8 units and centre at the intersection of the lines x+2y=8 and 2x-3y=5?
  
• Calculate the area between the curve y=3x-x^2 and the x axis between x=10 and x= 6?
  
• A particle moves in a straight line and its distance S(m) from a point is given by S=45t+11t-t^3. Find. expression of velocity in terms of t,the expression for acceleration in terms of t and the velocity and acceleration when t= 3 seconds?
  
• A particle moves in a straight line so that t seconds after passing through a fixed point O its velocity V m/s is given by the equation V=20t-2t^2 m/s.find the initial acceleration of the particle, the value of t when the particle is at rest?
  
• Calculate the area between the curve y=3x-x^2 and the axis between x=10 and x=6?
  
• Differentiate #sin y=xy^3+ylnx#?
  
• Integrate 3x-x^2, 6<x<10?
  
• Find the equations of the tangent and normal to the curve y=x^3-2x^2-2x-3 at x=2?
  
• Differentiate y=√√x?
  
• Differentiate Tan^-1y=x^3?
  
• Differentiate #y=x^3-4/(2x)+3#?
  
• Find the distance of the points A(3,6) B(-7,8) from the line 4x+6y-8=0?
  
• Find the inverse of the matrix #[[6,-2,-3],[-1,8,-7],[4,-4,6]]#?
  
• Differentiate y=x√x?
  
• Sketch and determine the turning points of the curve Y=1/3x^3-2x^2+3x+2?
  
• Differentiate #y=sqrt(x^2)+sqrt(4x)-sqrt3 ?
  
• Sketch and determine the turning points of the curve y=x^2-x+1?
  
• Find and classify all the turning points of y=2x^3+9x^2-24x-1?
  
• Sketch and determine the turning points of the curve y=12-12x+12x^2?
  
• Sketch and determine the turning points of the curve y=1/3x^3-2x^2+3x+2?
  
• Differentiate y=(x^2-5x)inx?
  
• Differentiate y=(x+1)cosx?
  
• Differentiate y=√[x^2+4x-3]?
  
• Differentiate (x^3-4)÷(2x+3)?
  
• Differentiate y =10(3x+1)(1-5x)?
  
• Given that 9y^2+25y^2=225,find the covertices and vertices,foci and length of the latus rectum?
  
• Express( 4,-4)in polar coordinates?
  
• Express (2,pie/6)in rectangular coordinates?
  
• Find x so that the distance between (x,3) and (2,-1)=5?
  
• Find the equation of the tangent to the circle x^2+y^2-2x+y-5=0 at(3-2)?
  
• Find the focus of the parabola y^2=1/2x^2-x+1/2?
  
• Differentiate x^4+y^4=8xy?
  
• Differentiate x^2+y^2=25?
  
• Write as polar coordinates( 2,2)?
  
• Show that [4-1 3][2 5-1][-8 2 6]is a singular matrix?
  
• Obtain the echlone form hence solve the equations x+2y+3z=-1 2x-y-2z=3 z+2y+2x=2?
  
• Find the inverse of the matrix [6 -2 -3][-1 8 -7][4 -4 6]?
  
• Find the focus and directrix of the parabola y^2=2a(x-a)?
  
• Find the distance of the points A(3,6)B(-7,8) from the line 4x+6y-8=0?
  
• Use gauss Jordan method to solve the systems of simultaneous below #4x-y+3z=11#, #2x+z=5#, #2z-3x+y=5#?
  
• Find the equation of the line joining points (3 8) and (7 5) and show that it passes through the point(15 -1)?
  
• Given the equation of a hyperpola #(x+2)^2/a-(y-1)^2/16=1# find the coordinates of c,the foci and the vertices?
  
• Show that a rectangle with area of 100cm^2 and minimum perimeter is a square?
  
• The circle c has the centre at (3,2) and passes through the point (2,1) determine whether the point with coordinates(4,7) lies on or in the circle ?
  
• Write a polar equation of the parabola with focus at the origin and directrix y=2?
  
• Find the equation of the tangent to the circle x²+y²-2x+y-5=0 at (3,-2)?
  
• The points A B C have coordinates (7,0),(3,-3),and (-3,3).find the coordinates of D E F the midpoints of BC,CA,AB respectively?
  
• Express r=4÷{3+4cos theta} as a Cartesian equation?
  
• A car starts from rest and moves a distance of 5m in t seconds ,where s=1/6t³+1/4t².find the acceleration when t=0,t=2?
  
• Using remainder theorem find the remainder when 7x³+40x²+22x-35is divided by( x+1)?
  
• Simplify without using tables or calculations {Sin²315°(1-tan²210°)}÷{(1+cos²120°)(1+tan²330°)}?
  
• Factorise 4x²+8xy+4y²?
  
• Find the values of R for which the equation have equal roots x²(R+2)x+R²=0?
  
• If alpha and beta are the roots of 2x²+7x-2=0 without solving form an equation whose roots are alpha squared and beta squared?
  
• Expand (1-3x)^8 in ascending power of x up to x³.hence using our expansion evaluate 0.97^8 correct to 5 decimal places.?
  
• (Log 49+log 343-log 2401)÷(log16807-log 7)?
  
• Evaluate log x³+log5x=5log2-log (2/5)?
  
• A company produces x bottles of beer.the profit from sales P(x)is given by the function P(x)=96x-6x²-234,find the maximum profit and the number of bottles that must be sold to realize that profit?
  
• Expand (1-3x)^8 in ascending power of x up to x³.hence solve 0.97^8 ?
  
• Prove sinh²+cosh²x=cosh2x?
  
• How do you explain the division of 222/22 to a young one using the long division method?
  
• The equation 4x²+8x-1=0 has its roots as alpha and beta.find the valuesof 1/alpha²+1/beta²?
  
• Convert 270°into radius?
  
• Prove that #""^nC_r=""^nC_(n-r)# hence solve #""^8C_4#?
  
• Find the domain in #y=sqrt(4-x)#?
  
• Evaluate dy/DX=2y²/x³?
  
• (dy/dx)-y=4y^5?
  
• Define Bernoulli's equation hence solve( dy/DX)+y/x=x²y^6?
  
• Find a complete solution in( d²y/dx²)-4dy/dx+13y=24e^2x+ sin 3x?
  
• Cos²xdy/dx+y=tan x?
  
• Solve the homogeneous ode 2xy²dy-(x³+2y³dx=0?
  
• Form a differential equation if #y=e^x#?
  
• Show that #y_1=x^2# is a solution to the differential equation #x^2y'' -(x^2+4x)y' +(2x+6)y=0 #?
  
• Solve xy^1+4y=x³y²?
  
• What is the general solution of the differential equation? : #(d^4y)/(dx^4) - 4 y = 0#
  
• #dy/dx+y/x=x^2y^6#?
  
• Find the initial value problem in #dy/dx=(y^2+4x^2)/(4xy)#?
  
• Explian the difference between "How many days are there between 10th may and 10th July"and how many days are there from 10th may to 10th July?